Find the formula for the nth element and the sum of the first 15 elements

| May 8, 2021 | education

Find the formula for the nth element and the sum of the first 15 elements of the arithmetic progression with the first element 3.4 and the difference 0.9.

Let’s use the formula of the nth term of the arithmetic progression an = a1 + (n – 1) * d, where a1 is the first term of the arithmetic progression, d is the difference of the arithmetic progression.

According to the condition of the problem, in this arithmetic progression, the first term is 3.4, and the difference is 0.9, therefore, we can write the formula for the nth term for this arithmetic progression:

аn = 3.4 + (n – 1) * 0.9 = 3.4 + 0.9 * n – 0.9 = 2.5 + 0.9 * n.

Substituting the sum of the first n members of the arithmetic progression Sn = (2 * a1 + d * (n – 1)) * n / 2 values ​​a1 = 3.4, d = 0.9, n = 15 into the formula, we find the sum of the first 15 elements of this arithmetic progression:

Sn = (2 * a1 + d * (15 – 1)) * 15/2 = (2 * a1 + d * 14) * 15/2 = 2 * (a1 + d * 7) * 15/2 = (a1 + d * 7) * 15 = (3.4 + 0.9 * 7) * 15 = (3.4 + 6.3) * 15 = 9.7 * 15 = 145.5.

Answer: the formula for the n-th element of this progression: аn = 2.5 + 0.9 * n; the sum of the first 15 elements of this arithmetic progression is 145.5.



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